British & Irish Lions scrum-half candidate Blair was taken off after 52 minutes against the Irish after suffering from a back spasm.
"Mike has been assessed today and his condition is improving. He had a comfortable night's sleep and is up and mobile," said Scottish team doctor James Robson, who will also travel with the Lions to South Africa this summer.
"He will be subject to further review tomorrow with a view to resuming running, hopefully on Wednesday."
Thom Evans (shoulder) and Alasdair Strokosh (neck) both received treatment after the 22-15 defeat at Murrayfield, but are expected to be fit for consideration for Saturday.